Prime Factorization  Grade 6
Prime Factorization examples and questions , with detailed solutions and explanations,
for grade 6 students are presented. A review of factors and multiples would be very helpful to understand prime factorization.
Prime Numbers
Definition: Any whole number that can be divided by 1 and itself ONLY is called a prime number.
Example 1
2 is a prime number, why?
2 can be divided by 1 2 ÷ 1 = 2 with remainder equal to zero
2 can be divided by 2 (itself) 2 ÷ 2 = 1 with remainder equal to zero
Try to find another whole number that divides 2 with remainder zero. There is not.
Example 2
7 is a prime number, why?
7 can be divided by 1 7 ÷ 1 = 7 with remainder equal to zero
7 can be divided by 7 (itself) 7 ÷ 7 = 1 with remainder equal to zero
Try to find another whole number that divides 7 with remainder zero. There is not.
The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
You can generate more prime numbers and test them.
Composite Numbers
Definition: Any whole number that can be divided (with remainder equal to zero) by another whole number other than 1 and itself is called composite number.
4 is a composite number, why?
4 can be divided by 1, itself and 2.
6 is a composite number, why?
6 can be divided by 1, itself, 2 and 3.
12 is a composite number : it can be divided by 1, itself, 2, 3, 4 and 6.
30 is a composite number: it can be divided by 1, itself, 2, 3, 5, 6, 10 and 15.
Factorization
From division to multiplication to factoring.
Division and multiplication are related operations.
The division 6 ÷ 3 = 2 may be written as a multiplication: 6 = 2 × 3
To factor a whole number is to write it as a product of two or more whole numbers.
Examples
1) 6 = 1 × 6 ; 6 = 2 × 3 1, 2, 3 and 6 are called factors of 6.
2) 12 = 12 ×1 = 3 ×4 = 6 ×2 1, 2, 3, 4, 6 and 12 are called factors of 12.
3) 20 = 1 × 20 = 2 ×10 = 2 × 2 × 5 = 4 × 5 1, 2, 3, 4, 5, 10 and 20 are called factors of 20.
Prime factorization
Prime factorization is to write a composite whole number as the product of prime numbers only.
Examples
1) 6 = 2 × 3 the factors 2 and 3 are prime numbers.
2) 12 = 2 × 2 × 3 the factors 2 and 3 are prime numbers.
3) 20 = 2 × 2 × 5 the factors 2 and 5 are prime numbers.
How to find prime factorization of composite number?
Example 1
Write the prime factorization of 12
1) See if the first prime number 2 is a factor of the given number 12
12 ÷ 2 = 6 with remainder = 0 2 is a factor of 12 12 = 2 × 6
2) See if the first prime number 2 is a factor of 6
6 ÷ 2 = 3 with remainder = 0 2 is a factor of 6 6 = 2 × 3 Hence 12 = 2 × 6 = 2 × 2 × 3
12 = 2 × 2 × 3 is completely factored using only prime numbers 2 and 3
Example 2
Write the prime factorization of 21
1) See if the first prime number 2 is a factor of the given number 21
21 ÷ 2 = 10 but remainder = 1 so 2 is not a factor of 21
2) Is the next prime number 3 a factor of 21?
21 ÷ 3 = 7 with remainder 0 3 is a factor of 21 21 = 3 × 7
3 and 7 are prime numbers and therefore 21 = 3 × 7 is completely factored using only prime numbers 3 and 7
This prime factor calculator can be used to generate all prime factors of a given number.
Answer the Following Questions

For each number below, decide which is a prime and which is a composite number? Explain.
 9
 11
 16
 22
 39
 41
 49
 57

Which of the following is a prime factorization?
 8 = 2 × 4
 10 = 2 × 5
 20 = 2 × 10
 30 = 2 × 3 × 5
 38 = 2 × 19
 42 = 2 × 3 × 7
 56 = 2 × 2 × 14
 75 = 3 ×25
 80 = 2 × 2 × 2 × 2 × 5
 100 = 2 × 2 × 25

What is the prime factorization to each of the following whole numbers?
 8
 18
 24
 45
 63
 88
 96
Solutions to the Above Problems

A prime number has only 2 factors: 1 and itself. A composite has 3 factors or more.
 9 is a composite number since 9 = 3 × 3 , it has 3 fators: 1, 3 and itself
 11 is a prime number because it has only 2 factors: 1 and itself
 16 is a composite number since 16 = 4 × 4 = 2 × 8 , it has 5 fators: 1, 2, 4 , 8 and itself
 22 is a composite number since 22 = 2 × 11 , it has 4 fators: 1, 2, 11 and itself
 39 is a composite number since 39 = 3 × 13 , it has 4 factors : 1, 3, 13 and itself
 41 is a prime number because it has only 2 factors: 1 and itself
 49 is a composite number since 49 = 7 × 7 , it has 4 factors : 1, 7 and itself
 57 is a composite number since 57 = 3 × 19 , it has 4 factors: 1, 3, 19 and itself

A prime factorization includes prime numbers only.
 8 = 2 × 4 the factor 4 is not a prime number therefore it is not a prime factrorization.
 10 = 2 × 5 both factors 2 and 5 are prime numbers so it is a prime factrorization.
 20 = 2 × 10 the factor 10 is not a prime number therefore it is not a prime factrorization.
 30 = 2 × 3 × 5 ; all factors 2, 3 and 5 are prime numbers so it is a prime factrorization.
 38 = 2 × 19 both factors 2 and 19 are prime numbers so it is a prime factrorization.
 42 = 2 × 3 × 7 all factors 2, 3 and 7 are prime numbers so it is a prime factrorization.
 56 = 2 × 2 × 14 the factor 14 is not a prime number therefore it is not a prime factrorization.
 75 = 3 × 25 the factor 25 is not a prime number therefore it is not a prime factrorization.
 80 = 2 × 2 × 2 × 2 × 5 all factors 2 and 5 are prime numbers so it is a prime factrorization.
 100 = 4 × 25 both factors are composite; it is not a prime factrorization.

Prime factorization is carried out by successive divions using prime numbers.
 8 = 2 × 4 = 2 × 2 × 2
 18 = 2 × 9 = 2 × 3 × 3
 24 = 2 × 12 = 2 × 2 × 6 = 2 × 2 × 2 × 3
 45 = 3 × 15 = 3 × 3 × 5
 63 = 7 × 9 = 7 × 3 × 3
 88 = 2 × 44 = 2 × 2 × 22 = 2 × 2 × 2 × 11
 96 = 2 × 48 = 2 × 2 × 24 = 2 × 2 × 2 × 12 = 2 × 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 2 × 3